On left and right bases of po-Gamma-semigroups

Wichayaporn Jantanan1 Department of Mathematics, Faculty of Science, Buriram Rajabhat University, Buriram31000, Thailand E-mail: [email protected]

Nipawan Trihera2 Department of Mathematics, Faculty of Science, Buriram Rajabhat University, Buriram31000, Thailand E-mail: [email protected]

Natee Raikham3 Department of Mathematics, Faculty of Science, Buriram Rajabhat University, Buriram31000, Thailand E-mail: [email protected]

Ronnason Chinram4 Algebra and Application Research Unit, Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla90110, Thailand E-mail: [email protected]

Pattarawan Petchkaew5 Mathematics Program, Faculty of Science and Technology, Songkhla Rajabhat University, Songkhla90000, ThailandCorrespondence[email protected]

Abstract

The concepts of left and right bases of Γ -semigroups were introduced by Changphas and Kummoon. In this paper, we introduce the concepts of the left and right bases of po- Γ -semigroups and extend the results in Γ -semigroups to po- Γ -semigroups. We focus on the structure of po- Γ -semigroups containing the right bases. In addition, we prove that all of the right bases of a po- Γ -semigroup have the same cardinality and conclude that a non- empty po- Γ -semigroup eliminating the union of its all right bases is a left Γ -ideal of such po- Γ -semigroup.

Subject Classification: (2010):

20M99

Keywords:

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On left and right bases of po-Gamma-semigroups

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